**2. Features of conductivity of semi-insulating CdTe and CdZnTe single crystals**

This section deals with the results of studies of CdTe crystals, doped with Cl and Cd0,9Zn0,1Te crystals, doped with In, which are widely used for the creation of detectors. The results of the research reveal important features of the electrical characteristics of the crystals. **Figure 1a** presents the typical temperature dependences of the resistivity *ρ*(*T*) of the CdTe [5–8] and CdZnTe [9, 10] crystals under study.

The temperature dependence of the intrinsic resistivity of CdTe and CdZnTe crystals *ρ*i (*T*) = 1/*qn*<sup>i</sup> (*μ*<sup>n</sup> + *μ*p) is also shown for comparison (where де *n*<sup>i</sup> = (*N*<sup>c</sup> *N*v )1/2exp(−*E*<sup>g</sup> /2*kT*) is the concentration of intrinsic charge carriers, *N*c = 2(*m*n*kT*/2*πħ*)3/2 and *N*v = 2(*m*p*kT*/2*πħ*)3/2 are the effective density of states in the conduction band and the valence band of the semiconductor, respectively). As seen, the values of *ρ* and *ρ*<sup>i</sup> of both CdTe and CdZnTe are quite close in the whole temperature range, which is important taking into account the necessity to minimize

gap in the whole temperature range, the thermal activation energy is much smaller than that of intrinsic semiconductor. Another important conclusion is that the Fermi level crosses the Fermi level in intrinsic Cd0,9Zn0,1Te at a temperature of ~330 K, that is the material changes the

Mechanisms of Charge Transport and Photoelectric Conversion in CdTe-Based X- and Gamma-Ray Detectors

An analysis of the statistics of electrons and holes in a semiconductor, in which donor defects form self-compensated complexes, provides additional information on the compensation mechanism in the CdTe and Cd0,9Zn0,1Te crystals. Consideration of the features of self-compensated semiconductors minimizes the number of independent parameters in the calculations [11]. It is important that the concentration of the donor impurity (Cl or In) is significantly higher than the concentration of background impurities and defects. Under this condition, calculations can be made using the simplified scheme of levels in the bandgap, namely, the deep donor and deep acceptor level, as well as the shallow level of donors that did not form complexes, that is, on the "three-level" compensation model [12]. In the electroneutrality equation for semi-insulating wide-band semiconductor with a high concentration of impurities (~1018 см−3), the concentration of free carriers *n* and *p* (which do not exceed 107

10<sup>8</sup> cm−3 even at elevated temperatures) can be neglected. It is natural to assume that the level of compensating acceptors is located in the lower part of the bandgap (or at least ~5*kT* below

ionization energy of 0.43–0.47 eV. With such simplifications, the electroneutrality equation is

Thus, the Fermi-level energy at a temperature *T* is determined by the energy of the donor level

the calculation according to Eq. 2 with the experimental dependences Δ*μ*(*Т*) obtained from the results of measurements of resistivity *ρ*(*Т*), as shown in **Figure 1c**. The best match of the calculated and experimental dependencies Δ*μ*(*Т*) corresponds to *Е*<sup>d</sup> = 1.081 eV, *ξ* = 0.99998 for Cd0,9Zn0,1Te and *Е*<sup>d</sup> = 0.783 eV, *ξ* = 0.976 for CdTe. The obtained values of ionization energy are in the range, in which the photoluminescence bands were detected, which is also consistent

methods. Obtained high degree of donor compensation *ξ* = 0.979 for CdTe and *ξ* = 0.99998 for Cd0,9Zn0,1Te confirms the known theoretical fact that an element of Group III or VII of the Periodic system (in this case, Cl and In) as a donor impurity introduced in the crystal lattice, causes the appearance of approximately the same amount of compensating intrinsic defects, which leads to the formation of complexes. It should be emphasized that the obtained values *ξ* are close to the degree of compensation provided by the Mandel theory for CdTe and ZnTe [13].

These results are important from a practical point of view: (1) At *Е*<sup>d</sup> = 0.60 eV (as in the crystal Cd0,9Zn0,1Te under study), the values of *ρ* become close to the maximum value in a very narrow range of *ξ* (**Figure 2a**). When shifting of the donor to the middle of band gap domeshaped curve *ρ*(*ξ*) expands and its maximum shifts toward values of *ξ*, close to 0.5. The achievement of the semi-insulating state Cd0,9Zn0,1Te *Е*<sup>d</sup> = 0.60 eV and *ξ* = 0.99998 became

with the results of the study of energy levels in the band gap CdTe and Cd1 <sup>−</sup> *<sup>x</sup>*

, and its analytical solution is

is the concentration of acceptors. Such acceptors may be Cd or Zn vacancies with

\_\_\_ 1 − *ξ*

the Fermi level), that is, they are almost completely ionized, and it can be taken *N*<sup>a</sup>

+

= *Ed* + kTln[

to

31

<sup>+</sup> ≈ *N*<sup>a</sup> ,

*<sup>ξ</sup>* ]. (2)

http://dx.doi.org/10.5772/intechopen.78504

Zn*<sup>x</sup>*

Te by other

/*N*d, which can be found by comparing the results of

type of conductivity.

where *N*<sup>a</sup>

reduced to the expression *N = N*<sup>d</sup>

*E*d and its compensation degree *ξ* = *N*<sup>a</sup>

**Figure 1.** (a) Temperature dependences of resistivity of the CdTe and Cd0,9Zn0,1Te crystals. Dashed lines show the temperature dependences of resistivity of CdTe and Cd0,9Zn0,1Te crystals with intrinsic conductivity *ρ*<sup>i</sup> , dotted lines show its maximum possible values *ρ*max. (b) Dependence of resistivity of CdTe on position of the Fermi level at different temperatures. The Fermi level energy Δ*μ*<sup>i</sup> in intrinsic CdTe is also shown. (c) Temperature dependences of the Fermi level energies in CdTe and CdZnTe crystals. Circles and squares show the values of Δ*μ* (*T*) calculated with Eq. (1). Solid lines show Δ*μ*calc(*T*) calculated with Eq. (2). Dashed lines show the Fermi levels in the intrinsic materials.

the dark current in X/γ-rays detectors. At temperatures above the room temperature (>320– 330 K), the resistivity *ρ* of CdTe crystal exceeds its value for a material with intrinsic conductivity *ρ*<sup>i</sup> . At temperatures below ~ 280 K, the resistivity of CdTe crystal exceeds the resistivity of Cd0,9Zn0,1Te with a wider (!) bandgap. The observed excess *ρ* over *ρ*<sup>i</sup> is explained, the much lower mobility of holes in comparison with the mobility of electrons. If the Fermi level shifts from its position in the intrinsic semiconductor toward the valence band, the contribution of holes into electrical conductivity increases and thus resistivity also increases. However, with further displacement of the Fermi level the resistivity decreases, as the concentration of holes becomes too large. As a result, the thermal activation energy of the electrical conductivity decreases. Giving *ρ* as 1/*q*(*nμ*<sup>n</sup> + *n*<sup>i</sup> 2 *μ*p/*n*) and equating to zero the derivative *dρ/dn*, is easy to show that the maximum value of the resistivity is determined by *ρ*max = (2*qn*<sup>i</sup> (*μ*n*μ*p)1/2)−1. As shown in **Figure 1b**, the value of the maximum possible resistivity *ρ*max significantly exceeds the intrinsic resistivity of CdTe crystal in the whole temperature range. In the case of a semiconductor with almost intrinsic conductivity, the solution of equation *ρ* = 1/*q*(*nμ*<sup>n</sup> + *pμ*p) for Fermi energy *Δμ* has the form as follows:

\*\*Fermi energy  $\Delta\mu$  has the norm as follows:

$$\Delta\mu = \text{kTh}\left(\frac{1 \pm \sqrt{1 - 4\rho^2 \rho^2 \mu\_s \mu\_p n\_i^2}}{2q\rho \,\mu\_s n\_i^2/N\_v}\right) \tag{1}$$

where "+" and "−" correspond to n- and p-type semiconductor, respectively. That is, one can find the Δ*μ*(*Т*) dependences of the crystals under study (**Figure 1c**) from the temperature dependence of the resistivity *ρ*(*Т*) (**Figure 1a**), taking into account the temperature dependences of *n*<sup>і</sup> and mobilities of electrons *μ*n and holes *μ*p [5]. The Fermi-level energy of the samples calculated with Eq. (1) (**Figure 1c**) shows that the Fermi level is noticeably removed from the conduction band when temperature increase, which slows the growth of the electrons concentration, consequently, leads to a decrease in the of thermal activation energy. As a consequence, despite the fact that the Fermi level located near the middle of the band gap in the whole temperature range, the thermal activation energy is much smaller than that of intrinsic semiconductor. Another important conclusion is that the Fermi level crosses the Fermi level in intrinsic Cd0,9Zn0,1Te at a temperature of ~330 K, that is the material changes the type of conductivity.

An analysis of the statistics of electrons and holes in a semiconductor, in which donor defects form self-compensated complexes, provides additional information on the compensation mechanism in the CdTe and Cd0,9Zn0,1Te crystals. Consideration of the features of self-compensated semiconductors minimizes the number of independent parameters in the calculations [11]. It is important that the concentration of the donor impurity (Cl or In) is significantly higher than the concentration of background impurities and defects. Under this condition, calculations can be made using the simplified scheme of levels in the bandgap, namely, the deep donor and deep acceptor level, as well as the shallow level of donors that did not form complexes, that is, on the "three-level" compensation model [12]. In the electroneutrality equation for semi-insulating wide-band semiconductor with a high concentration of impurities (~1018 см−3), the concentration of free carriers *n* and *p* (which do not exceed 107 to 10<sup>8</sup> cm−3 even at elevated temperatures) can be neglected. It is natural to assume that the level of compensating acceptors is located in the lower part of the bandgap (or at least ~5*kT* below the Fermi level), that is, they are almost completely ionized, and it can be taken *N*<sup>a</sup> <sup>+</sup> ≈ *N*<sup>a</sup> , where *N*<sup>a</sup> is the concentration of acceptors. Such acceptors may be Cd or Zn vacancies with ionization energy of 0.43–0.47 eV. With such simplifications, the electroneutrality equation is reduced to the expression *N = N*<sup>d</sup> + , and its analytical solution is

the dark current in X/γ-rays detectors. At temperatures above the room temperature (>320– 330 K), the resistivity *ρ* of CdTe crystal exceeds its value for a material with intrinsic conduc-

**Figure 1.** (a) Temperature dependences of resistivity of the CdTe and Cd0,9Zn0,1Te crystals. Dashed lines show the

its maximum possible values *ρ*max. (b) Dependence of resistivity of CdTe on position of the Fermi level at different

level energies in CdTe and CdZnTe crystals. Circles and squares show the values of Δ*μ* (*T*) calculated with Eq. (1). Solid

temperature dependences of resistivity of CdTe and Cd0,9Zn0,1Te crystals with intrinsic conductivity *ρ*<sup>i</sup>

lines show Δ*μ*calc(*T*) calculated with Eq. (2). Dashed lines show the Fermi levels in the intrinsic materials.

lower mobility of holes in comparison with the mobility of electrons. If the Fermi level shifts from its position in the intrinsic semiconductor toward the valence band, the contribution of holes into electrical conductivity increases and thus resistivity also increases. However, with further displacement of the Fermi level the resistivity decreases, as the concentration of holes becomes too large. As a result, the thermal activation energy of the electrical conductivity

shown in **Figure 1b**, the value of the maximum possible resistivity *ρ*max significantly exceeds the intrinsic resistivity of CdTe crystal in the whole temperature range. In the case of a semiconductor with almost intrinsic conductivity, the solution of equation *ρ* = 1/*q*(*nμ*<sup>n</sup> + *pμ*p) for

> \_\_\_\_\_\_\_\_\_\_\_\_\_ 1 − 4 *q* <sup>2</sup> *ρ*<sup>2</sup> *μ<sup>n</sup> μ<sup>p</sup> ni*

\_\_\_\_\_\_\_\_\_\_\_\_\_ 2q*<sup>ρ</sup> <sup>μ</sup><sup>n</sup> ni*

and mobilities of electrons *μ*n and holes *μ*p [5]. The Fermi-level energy of the

<sup>1</sup> <sup>±</sup> <sup>√</sup>

where "+" and "−" correspond to n- and p-type semiconductor, respectively. That is, one can find the Δ*μ*(*Т*) dependences of the crystals under study (**Figure 1c**) from the temperature dependence of the resistivity *ρ*(*Т*) (**Figure 1a**), taking into account the temperature depen-

samples calculated with Eq. (1) (**Figure 1c**) shows that the Fermi level is noticeably removed from the conduction band when temperature increase, which slows the growth of the electrons concentration, consequently, leads to a decrease in the of thermal activation energy. As a consequence, despite the fact that the Fermi level located near the middle of the band

of Cd0,9Zn0,1Te with a wider (!) bandgap. The observed excess *ρ* over *ρ*<sup>i</sup>

2

show that the maximum value of the resistivity is determined by *ρ*max = (2*qn*<sup>i</sup>

. At temperatures below ~ 280 K, the resistivity of CdTe crystal exceeds the resistivity

*μ*p/*n*) and equating to zero the derivative *dρ/dn*, is easy to

in intrinsic CdTe is also shown. (c) Temperature dependences of the Fermi

2

<sup>2</sup> /*Nv* ), (1)

is explained, the much

, dotted lines show

(*μ*n*μ*p)1/2)−1. As

tivity *ρ*<sup>i</sup>

dences of *n*<sup>і</sup>

decreases. Giving *ρ* as 1/*q*(*nμ*<sup>n</sup> + *n*<sup>i</sup>

temperatures. The Fermi level energy Δ*μ*<sup>i</sup>

30 New Trends in Nuclear Science

Fermi energy *Δμ* has the form as follows:

= kTln(

$$
\Delta\mu = E\_d + \text{kTh}\left[\frac{1-\xi}{\xi}\right].\tag{2}
$$

Thus, the Fermi-level energy at a temperature *T* is determined by the energy of the donor level *E*d and its compensation degree *ξ* = *N*<sup>a</sup> /*N*d, which can be found by comparing the results of the calculation according to Eq. 2 with the experimental dependences Δ*μ*(*Т*) obtained from the results of measurements of resistivity *ρ*(*Т*), as shown in **Figure 1c**. The best match of the calculated and experimental dependencies Δ*μ*(*Т*) corresponds to *Е*<sup>d</sup> = 1.081 eV, *ξ* = 0.99998 for Cd0,9Zn0,1Te and *Е*<sup>d</sup> = 0.783 eV, *ξ* = 0.976 for CdTe. The obtained values of ionization energy are in the range, in which the photoluminescence bands were detected, which is also consistent with the results of the study of energy levels in the band gap CdTe and Cd1 <sup>−</sup> *<sup>x</sup>* Zn*<sup>x</sup>* Te by other methods. Obtained high degree of donor compensation *ξ* = 0.979 for CdTe and *ξ* = 0.99998 for Cd0,9Zn0,1Te confirms the known theoretical fact that an element of Group III or VII of the Periodic system (in this case, Cl and In) as a donor impurity introduced in the crystal lattice, causes the appearance of approximately the same amount of compensating intrinsic defects, which leads to the formation of complexes. It should be emphasized that the obtained values *ξ* are close to the degree of compensation provided by the Mandel theory for CdTe and ZnTe [13].

These results are important from a practical point of view: (1) At *Е*<sup>d</sup> = 0.60 eV (as in the crystal Cd0,9Zn0,1Te under study), the values of *ρ* become close to the maximum value in a very narrow range of *ξ* (**Figure 2a**). When shifting of the donor to the middle of band gap domeshaped curve *ρ*(*ξ*) expands and its maximum shifts toward values of *ξ*, close to 0.5. The achievement of the semi-insulating state Cd0,9Zn0,1Te *Е*<sup>d</sup> = 0.60 eV and *ξ* = 0.99998 became possible due to doping by self-compensated donors and the formation of A- or DX-centers, the concentration of which is practically equal to the concentration of acceptors due to the very nature of these centers. (2) In a certain combination of ionization energy and the compensation degree, changes in the temperature dependence of resistivity and/or inversion of the conductivity type of the crystal in the climate-change temperature range may occur that may affect on the operation of the X/γ-ray detector with the Schottky diode. If the donor level located near the middle of the band gap of the Cd0,9Zn0,1Te crystal (*E*<sup>d</sup> = 0.7 eV), to obtain the resistivity *ρ* = 1010 Ω·сm at 300 К (**Figure 2b**), the compensation degree equals to *ξ* = 0.679, and the thermal activation energy of conductivity is close to the half of the Cd0,9Zn0,1Te band gap at 0 K (Δ*E* = 0.84 eV). If *E*<sup>d</sup> = 0.5 eV to ensure *ρ* = 1010 Ω·сm at 300 K, the compensation level should be increased to 0.99979, which leads to a decrease of Δ*E* to 0.65 eV. When *E*<sup>d</sup> = 0.3 eV, the compensation degree should further increase to 0.9999999, making activation energy decreases to 0.47 eV. If *E*d equals to 0.9 eV to ensure *ρ* = 1010 Ω·сm, the compensation degree should be considerably less than 1/2, namely *ξ* = 0.00047. In this case, the thermal activation energy Δ*E* will be 1.04 eV, that is, it becomes "abnormally" high [5, 7, 9].

climate-change temperature range, which is observed at an intermediate value of *ξ* = 0.99999. Unlike Cd0,9Zn0,1Te with a high compensation degree, in CdTe crystals the compensation degree is much lower and the dependence of the Fermi level on *ξ* is much weaker. Therefore, in CdTe, the transition from p- to n-type of conductivity occurs at an increase from 0.90 to 0.99, that is, by 9%, while in Cd0,9Zn0,1Te—only by 0.01%. This explains how much harder is to

Mechanisms of Charge Transport and Photoelectric Conversion in CdTe-Based X- and Gamma-Ray Detectors

http://dx.doi.org/10.5772/intechopen.78504

33

The operation of CdTe detector in spectrometric mode assumes complete collection of the charge generated by the absorption of high-energy quanta. Since the lifetime of charge carriers in the most perfect CdTe crystals does not exceed several microseconds, it is necessary to apply a rather high voltage to prevent the "capture" of the carriers by deep impurities (defects). At low voltage applied to the CdTe crystal with ohmic contacts, *I-V* characteristic is linear, but at higher bias a superlinear increase in current is always observed [14]. Attention is drawn to the fact that the deviation from linear *I-V* relationships at higher voltage is observed stronger when the temperature decreases (**Figure 3b**, inset). Therefore, we can assume that an additional charge transport mechanism with much weaker temperature dependence comes into play with increasing voltage. This is confirmed by the data in **Figure 3b**, which show the voltage dependences of the difference Δ*I* between the measured current *I* and a linearly

current is virtually independent of temperature. A deviation of *I-V* characteristics from linearity due to lowering the barrier at imperfect Ohmic contact should be rejected because such a mechanism leads to an exponentially increase in the current with temperature [15]. The current caused by tunneling transitions of electrons from the Fermi level in the metal (or slightly below it) into the semiconductor can be almost temperature independent [16]. However, at bias voltage in the range 10–100 V, the probability of tunneling is practically zero. A much greater probability of tunneling is through a thin interfacial oxide layer, whose presence on the crystal surface before metal deposition cannot be excluded (**Figure 3c**). At higher voltages, the linear behavior of the *I-V* characteristic of the CdTe crystal is replaced by a quadratic dependence on *V*, as in the case of space charge limited current (SCLC)] according to the Mott-Gurney law [17]. It is confirmed by comparing the experimental data with the extrapolation of the quadratic *I-V* dependence (**Figure 3b**). According to theory, SCLC can be formed by injection of charge carriers into the valence or conduction band. In the case of semi-insulating CdTe, the injection of electrons into the conduction band should be preferred. Firstly, the excess concentration of electrons above the electron equilibrium concentration is achieved much easier, since in the CdTe:Cl crystals the electron concentration approximately two orders of magnitude lower than that of holes. Second, the electron mobility in CdTe is more than an order of magnitude higher than that of holes, and the SCLC is proportional to the charge carrier mobility. Finally, the electron current injected by tunneling is almost temperature independent, that is, observed from the experience and just this one needs to explain. Taking into account the current of thermally generated holes and SCLC we

). As seen, the current excessive over linearly extrapolated

grow a homogeneous Cd0,9Zn0,1Te crystal in comparison with CdTe.

(Δ*I = I* – *I*<sup>o</sup>

extrapolated current *I*<sup>o</sup>

can write:

**3. Charge collection efficiency in CdTe-based Ohmic detectors**

**Figure 2c** shows the calculated temperature dependences of the Fermi level energy in Cd0,9Zn0,1Te at different compensation degrees of donor (In) with ionization energy *Е*<sup>d</sup> = 0.45 eV, which corresponds to the often observed in these crystals photoluminescence band (~1.08 eV). The position of the Fermi level in the intrinsic Cd0,9Zn0,1Te is shown by dashed line. As seen, the Fermi level is located above the Fermi level in the intrinsic semiconductor at the compensation degree *ξ* = 0.9999 in the whole temperature range, that is, the semiconductor has an n-type of conductivity. At sufficiently higher compensation degree (*ξ* = 0.999999), the Fermi level is located below the Fermi level in the intrinsic Cd0,9Zn0,1Te, that is, the crystal has p-type conductivity [9]. It is also possible the condition when type of conductivity changes in the

**Figure 2.** (a) The dependence of resistivity of Cd0.9Zn0.1Te crystal on the compensation degree *ξ.* (b) Temperature dependences of resistivity *ρ* at the different ionization energies *E*d and compensation degree *ξ* = *N*<sup>a</sup> */N*d, which provides the same *ρ,* but different thermal activation energies Δ*E*. (c) The temperature dependences of the Fermi level energy Δ*μ* (*T*) in Cd0.9Zn0.1Te crystal at the different compensation degrees (Δ*μ*<sup>і</sup> - is the Fermi level energy in a crystal with intrinsic conductivity).

climate-change temperature range, which is observed at an intermediate value of *ξ* = 0.99999. Unlike Cd0,9Zn0,1Te with a high compensation degree, in CdTe crystals the compensation degree is much lower and the dependence of the Fermi level on *ξ* is much weaker. Therefore, in CdTe, the transition from p- to n-type of conductivity occurs at an increase from 0.90 to 0.99, that is, by 9%, while in Cd0,9Zn0,1Te—only by 0.01%. This explains how much harder is to grow a homogeneous Cd0,9Zn0,1Te crystal in comparison with CdTe.
